Understanding the FVE Algorithm (Part 2)
Recap
Before we present new content, we want to start with a quick summary of the key points from last week’s blog as a warm up. Over the next few weeks we are outlining the algorithmic concepts and mechanisms which underlie the Fair Value Estimator, and the FVEr Trading Strategy. Last week (Part 1 of the series) we covered:
The Main Assumption: Over long time intervals, a US based broad market or sector ETF has an innate and relatively consistent exponential growth rate. This rate is impacted by various factors, such as the market capitalization size of its constituents or the particular business attributes of its members. We examined two ETFs, IVE (iShares S&P 500 Value) and IJT (iShares S&P Small-Cap 600 Growth), to provide context.
From Assumption to Algorithm: Next, we discussed how to go from the above assumption to an algorithm that captures an exponential growth phenomenon, and introduced the term exponential regression (or exponential best fit) as the main modeling technique. We mentioned two examples of simplistic attempts at using exponential regression to model the price of the S&P 500, and discussed their shortcomings, such as starting point bias.
Understanding the FVE Algorithm (Part 2)
In the next few weeks of our blog series, we’ll explain exponential regression from the ground up, and then explain how the FVE algorithm employs an “ensemble method” to analyze thousands of regression curves over different time subintervals, and layers on top a filtering strategy to disregard outlier data.
As mentioned last week, exponential growth occurs when a quantity (in this case the price of an ETF or market index) is growing at the same percent rate each year, say 10%. We can develop a formula to model this as follows. Suppose that an investor starts with $100, and their investment grows at exactly 10% each year. Let’s look at their net worth over time:
This last expression implies that the logarithmic of the net worth of the investor grows linearly, where the y-intercept is 2, and the slope is log based 10 of 1.1. Or to put it another way, on a logarithmic scale the net worth of the investor is a line, not a curve. This is a very powerful observation, which provides the basis for exponential regression, or best fit.
As we mentioned last time, clearly the price of an ETF doesn’t grow exactly exponentially every day, week, and year, nor does the ETF announce to its investors what its growth rate will be in the future. This has to be modeled using an algorithm. But we are now armed with some tools.
The way we can determine if the price of an ETF is growing exponentially is by converting it to a logarithmic scale, and seeing if the corresponding data points look approximately like a line. If they do, then the original price is admitting exponential growth behavior.
The workflow then to calculate an exponential regression equation goes as follows:
Convert the price (over the desired time interval) of the ETF to logarithmic scale.
Use a statistical tool (namely something called the correlation coefficient) to test the linearity of the data points.
If the data points pass this linearity test, use least squares linear regression to calculate the best fit line through the linearized data points.
Undo the logarithmic function by applying the inverse function (or exponential function) to the best fit line to regain the original scale.
The resulting curve is called a best fit exponential function, or exponential regression curve.
Calculating a least squares linear regression (bullet point 3 above) when there are thousands of data points is only feasibly possible with computers, and involves minimizing the squared vertical distance between each data point and the presumptive best fit line, via calculus. As we discuss next week, for each week going back in time, our FVE algorithm calculates hundreds of linear regressions, each with hundreds of data points, making the process extremely computationally intensive.
After the close on Friday each week, we rent cloud space on Digital Ocean, a high performance computing platform, to run the algorithm for all the ETFs in our coverage universe. For those interested, Digital Ocean is a publicly traded company (DOCN), and has a similar business model as the newly IPO’d company CoreWeave, which provides access to Nvidia GPUs in their data centers for powering AI applications.
We are currently using a combination of the R coding language (popular in statistics), and python (popular in many applications including data science, and quant finance) to run the algorithm. One of the reasons we need to charge a subscription for our project is to offset the cost of server time.
Investing for the Long Run
The journalist Jeff Sommer of the New York Times wrote a great article this week about the power of investing in diversified index funds titled “A Recipe for Doubling Your Stock Returns, Again and Again,” with the first two paragraph being:
“Forget about the upheaval in the Middle East. Don’t dwell on Russia’s war with Ukraine, U.S. tariffs and the budget deficit — or just about anything else that has been dominating news coverage and threatening to undermine the markets.
These issues are critical right now, undeniably. But history suggests that they will be irrelevant in your investing life, if your horizon is long enough.”
For a passive index investor who has a long time horizon (and our strategy at FVEr Invest is specifically designed for those people), near term macroeconomic or geopolitical headlines (while not unimportant), will likely have little impact on a diversified index fund portfolio over a 20+ year time horizon. Broad market and sector ETFs have displayed incredibly consistent growth rates over long periods of time, and downward deviations from these trajectories provide an opportunity to supercharge long term returns, by taking more risk. This can be achieved through using some exposure to leveraged ETFs, or simply allocating more capital during those times, if possible.
In next week’s blog, we’ll break down a reasonable projection of how your money will grow if you allocate $50 a week into the FVEr Trading Strategy over the course of a 20 year time period. We think $50 is a reasonable amount of money to invest per week for a number of Americans.
FVEr Live Trading Monthly Update:
The end of trading today marks the close of Q2 2025, and what a quarter of volatility it turned out to be. The “Liberation Day” trade tariff announcement on April 2 roiled US equity markets, sending the S&P 500 down around 20%, before it clawed its way back to record highs last week. In mid April we began live trading our FVEr strategy, and rolled out the strategy to 6 broad market ETFs over the course of the quarter:
SPY (SPDR S&P 500)
IJH (iShares S&P Midcap 400)
IJR (iShares S&P Smallcap 600)
IWM (iShares Russell 2000)
QQQ (Invesco Nasdaq 100)
DIA (SPDR Dow Jones Industrial Average)
At the end of each month we will update how the strategies are performing, or more frequently if there is an important development. Each strategy started with $10,000 paper money using the API friendly brokerage firm, Alpaca. For each ticker, we run a control strategy which is in the underlying benchmark, a 2x leverage strategy, and a 3x leverage strategy (available for all ETFs except IJR). We apply the same rules based strategy to every ETF, which we will cover in detail in a future blog. Our co-founders are also employing this strategy with their own real money, because we believe it's important to “eat our own cooking,” and we believe in its potential. You can see the performance of the strategies below since their inception dates.
FVEr Weekly Market Update: June 30, 2025
Current Allocation Status: As of our model updates on Friday, the allocation status of the FVEr Trading Strategy remains mostly unchanged:
IJR (iShares S&P Small-Cap 600) and XLV (SPDR S&P 500 Healthcare) still have leveraged status.
The SPDR S&P Consumer Staples ETF (XLP) has also moved into leveraged status. Even though this ETF is only 4.81% undervalued, it has dipped enough over the last month to trigger our simple moving average (SMA) undervalued criteria, which is a secondary signal that can prompt the leveraged status. This signal is usually more of a transient signal that indicates the model thinks there is a “buy the dip” opportunity.
All other ETFs on our allocation page have the unleveraged status.
Market Valuations: The US stock market continues to appear neutrally valued, broadly speaking, with small-cap ETFs continuing to be the most undervalued according to our model. We encourage you to check out the “Spread Model” tab on the Models page, where you can see that the growth equities are on the cusp of looking moderately expensive relative to value equities.
See you next week. In the meantime, please don't hesitate to reach out if you have any questions.
The FVEr Team
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To schedule your session, simply email us at info@fverinvest.com with the subject line: "Learning Session". (Please note: We do not provide specific investment advice.)
